If you are asking which US President was the first to use a cell phone, just like "which US President was the first to use electricity (Benjamin Harrison), then I do not know the answer. Otherwise, I do believe that a federal law prohibits a sitting US President from "owning" or "subscribing" to a cellular service. I'm sure he's allowed to use the phones belonging to his aides, or his wife. He just cannot carry one as if it were his own. I'm uncertain on the authenticity of this information.
There is no restriction on the owning of a cell phone by a President. However, there are strict laws regarding retention of Presidential records - that is, everything a President does (in their official capacity) must be recorded and archived. Thus, a President can't use a traditional cell phone service. Nothing prevents them from using a cellular phone specially provided to him by the NSA (or other agency, which support the required recording and secure communications features).
To answer the original question, there is no known answer; commercial cell phones were relatively available starting in the 1980s, so any president from Reagan onward would be a candidate for first use of a cell phone.
President Obama is the first one to be known to commonly use a modern cell phone, particularly as a part of his 2008 campaign for the presidency. As noted above, however, once he became President, he was required to give up his normal commercial cell service.